Energy
and Other Constraints on a 3I/Atlas Type Object, if it is of
Artificial Origin
There have been speculations that the interstellar object 3I/Atlas
might be of artificial origin, rather than being a natural object.
This is obviously highly contentious, but I thought it would be
interesting to see just how likely it would be for a civilization
much like the Earth’s to send an object on an interstellar journey.
Even now, we know that Earth has already sent an interstellar
object or two on their way out of the solar system. These are rather
small probes, such as Voyager, Pioneer or New Horizons, that were
sent to study the outer planets and as a result of those missions,
are now proceeding out of the solar system. So, clearly it can be
done, though it must be kept in mind that gravity assists (so called
sling-shots) increased the velocity of these craft, such that they
were significantly faster than they would have been with launch
energy alone. That required some very specific orbital manoeuvres
and planetary alignments – those conditions would not necessarily
exist for other hypothetical journeys out of our solar system or out
of any similar solar system.
Energy Constraints
So, I did a very high-level (i.e. approximate) analysis of the
energy budget possible for a craft, using the energy various sources
that we now have or could soon have, here on Earth. Those are:
Energy Available
Fuel Mass Density (Kg/M3) Energy Density MJ/Kg
Methalox
(Methane/Oxy) 810 10
RP-1 with
Oxidizer 2074 12
Hydrogen, Liquid &
LOX 641 17
U-235 (25%
enriched) 4000 3,900
Hydrogen, Fusion
(DT) 4000 15,600
Here are the escape velocities from some points within the Solar
System.
Energy Required to Escape the Solar System
Initial Point Escape Velocity (km/sec)
Earth 42.1
Mars 34.1
Ceres 25.3
Jupiter 18.5
Saturn 13.6
Uranus 9.6
Neptune 7.7
Pluto 6.6
The basic idea is simple (below is the example of a 10 km radius
"spacecraft", similar to the 3I/Atlas speculations):
given a radius for the object, calculate the volume (assuming
a sphere)
make some of this the fuel mass and some of it the object
mass, using representative densities for both.
This example postulates a very high porosity in which a
metholox (liquid methane and liquid oxygen mix) fuel supply could be
contained.
Radius
- km 10
- m 10,000
Volume
(assuming sphere)
- km3 4,189
- m3 4.19E+12
Mass (kg)
Fuel
Methalox
- mass density
(kg/m3) 810
- porosity 90%
- total fuel
mass 3.05E+15
Non-Fuel
(rock/metal)
- mass density
(kg/m3) 3,000
- pct
non-porosity 10%
- total non-fuel
mass 1.26E+15
Total Fuel &
Non-Fuel Mass
- porosity 90%
-
Mass 4.31E+15Energy
Energy density
(MJ/kg) 10.0
- Total (max
avail, MJ) 3.05E+16
- porosity 90%
- Total, given
porosity est. (MJ) 2.75E+16
For a very rough
estimate of the velocity that could be obtained by burning this much
fuel, given the mass of the object, a simple kinetic energy
calculation is used. This assumes that all of the available energy
could be "somehow" converted to the kinetic energy of the
object:
Escape
Velocity (km/sec)
- from solar
system
Starting at Pluto
- km/sec 6.6
- m/sec 6,600
Escape Velocity –
Kinetic Energy Required
- from solar
system
Earth
- 6.65E+16
MJ
So, about 6.6 X
10E16 megajoules would be needed, but only about 2.8 X 10E16
megajoules would be available, even given simplistic and
unrealistically optimistic estimates of the theoretically available
energy. That gives an Energy Available/Required ratio of only about
0.41, not even half of what is needed to escape the solar system,
even from the distance of Pluto.
Perhaps a
significant payload could be launched out of a sun-like star’s
solar system with a long series of gravity assists, though that would
probably be extremely complicated and time consuming. Perhaps a long
series of "stepping stones" might work, moving slowly to
the outer parts of the system, always making use of local resources,
such as dwarf planets, comets and asteroids.
However, if
nuclear energy could be used, the situation would be dramatically
different, due to the huge energy density of nuclear energy sources.
Even from Earth distance, it could probably be done if enough
enriched uranium was available and the object was assembled far from
the Earth’s gravitational influence. I think the surface or
near-surface of the object would have to be festooned with nuclear
reactors, at least of the power of hundreds of nuclear submarines.
At any rate, the energy would potentially be there, if it could be
converted into kinetic energy (maybe by accelerating ions in a strong
electric field).
The case is
improved further, if the object was powered by fusion energy from
deuterium-tritium reactors, should those actually be feasible. The
main advantage would be availability of fuel. That would be even
more true for deuterium- deuterium reactors. Again, the object’s
surface and near-surface would probably have to contain hundreds of
such reactors and devices for accelerating ions in strong electrical
fields.
Detailed
calculations for several fuels and several solar system distances
from the sun are given in an appendix at the end of the blog.
Other Constraints
The next obvious
question is "who would want to do this, given the vast expenses
and the long time scales involved?". After all, even at
fantastic velocities (e.g. 1000 km/sec) it would take millennia to
get anywhere interesting. (e.g. at about 30 billion km per year, it
would take about 1000 years to get to Alpha Centauri).
I think it would
have to be a long-lived species, very possibly a non-organic one,
that could make plans and then execute those plans on time scales
like this. That assumes that members of a machine species could
actually exist without breakdown for those kinds of time scales. On
Earth, I don’t think we have kept any machine running for even
centuries, let alone millennia.
So, my conclusion
is that something like 3i/Atlas could conceivably be artificial, but
it would indicate many technologies that we have still not achieved
and planning horizons and motivations that we can’t even begin to
comprehend.
That said, I
suppose if something is possible, it might well be done, eventually.
Appendix
Below is a table
with back-of-the-envelope calculations for various types of fuel and
various distances from the sun-like central star.
Assuming Asteroid Radius=10 km
|
|
|
|
|
|
Starting from 1 AU (Earth Distance)
|
|
|
|
|
|
Initial Point
|
Earth
|
Earth
|
Earth
|
Earth
|
Earth
|
Initial Point escape Velocity
|
42.1
|
42.1
|
42.1
|
42.1
|
42.1
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
2.71E+18
|
6.93E+18
|
2.14E+18
|
1.34E+19
|
1.34E+19
|
Energy Index (Avail/Required)
|
0.010
|
0.012
|
0.017
|
3.96
|
15.84
|
|
|
|
|
|
|
Starting from 1.52 AU (Mars Distance)
|
|
|
|
|
|
Initial Point
|
Mars
|
Mars
|
Mars
|
Mars
|
Mars
|
Initial Point escape Velocity
|
34.1
|
34.1
|
34.1
|
34.1
|
34.1
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
1.78E+18
|
4.55E+18
|
1.40E+18
|
8.77E+18
|
8.77E+18
|
Energy Index (Avail/Required)
|
0.015
|
0.019
|
0.026
|
6.04
|
24.15
|
|
|
|
|
|
|
Starting from 2.77 AU (Ceres Distance)
|
|
|
|
|
|
Initial Point
|
Ceres
|
Ceres
|
Ceres
|
Ceres
|
Ceres
|
Initial Point escape Velocity
|
25.3
|
25.3
|
25.3
|
25.3
|
25.3
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
9.77E+17
|
2.50E+18
|
7.73E+17
|
4.83E+18
|
4.83E+18
|
Energy Index (Avail/Required)
|
0.028
|
0.034
|
0.05
|
10.97
|
43.87
|
|
|
|
|
|
|
Starting from 5.2 AU (Jupiter)
|
|
|
|
|
|
Initial Point
|
Jupiter
|
Jupiter
|
Jupiter
|
Jupiter
|
Jupiter
|
Initial Point escape Velocity
|
18.5
|
18.5
|
18.5
|
18.5
|
18.5
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
5.23E+17
|
1.34E+18
|
4.14E+17
|
2.58E+18
|
2.58E+18
|
Energy Index (Avail/Required)
|
0.05
|
0.06
|
0.09
|
20.51
|
82.05
|
|
|
|
|
|
|
Starting from 9.6 AU (Saturn)
|
|
|
|
|
|
Initial Point
|
Saturn
|
Saturn
|
Saturn
|
Saturn
|
Saturn
|
Initial Point escape Velocity
|
13.6
|
13.6
|
13.6
|
13.6
|
13.6
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
2.82E+17
|
7.23E+17
|
2.23E+17
|
1.39E+18
|
1.39E+18
|
Energy Index (Avail/Required)
|
0.10
|
0.12
|
0.16
|
37.95
|
151.82
|
|
|
|
|
|
|
Starting from 19.2 AU (Uranus)
|
|
|
|
|
|
Initial Point
|
Uranus
|
Uranus
|
Uranus
|
Uranus
|
Uranus
|
Initial Point escape Velocity
|
9.6
|
9.6
|
9.6
|
9.6
|
9.6
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
1.41E+17
|
3.60E+17
|
1.11E+17
|
6.95E+17
|
6.95E+17
|
Energy Index (Avail/Required)
|
0.20
|
0.24
|
0.33
|
76.17
|
304.69
|
|
|
|
|
|
|
Starting from 30.0 AU (Neptune)
|
|
|
|
|
|
Initial Point
|
Neptune
|
Neptune
|
Neptune
|
Neptune
|
Neptune
|
Initial Point escape Velocity
|
7.7
|
7.7
|
7.7
|
7.7
|
7.7
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
9.05E+16
|
2.32E+17
|
7.16E+16
|
4.47E+17
|
4.47E+17
|
Energy Index (Avail/Required)
|
0.30
|
0.37
|
0.51
|
118.40
|
473.60
|
|
|
|
|
|
|
Starting from 39.5 AU (Pluto)
|
|
|
|
|
|
Initial Point
|
Pluto
|
Pluto
|
Pluto
|
Pluto
|
Pluto
|
Initial Point escape Velocity
|
6.6
|
6.6
|
6.6
|
6.6
|
6.6
|
Fuel
|
Methalox
|
RP-1 with Oxidizer
|
Hydrogen, Liquid & LOX
|
U-235 (25% enriched)
|
Hydrogen, Fusion (DT)
|
Porosity
|
90%
|
90%
|
90%
|
90%
|
90%
|
Energy Available:
|
2.75E+16
|
8.47E+16
|
3.68E+16
|
5.29E+19
|
2.12E+20
|
Energy Required:
|
6.65E+16
|
1.70E+17
|
5.26E+16
|
3.28E+17
|
3.28E+17
|
Energy Index (Avail/Required)
|
0.41
|
0.50
|
0.70
|
161.16
|
644.63
|
----------------------------------------------------------------------------------------------------------------------------------------------
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